Algorithm unfolding (or unrolling) was first proposed as an application of a parametric function to approximate the iterative soft-thresholding algorithm [1]}. The idea is to unfold the iterations as a cascade of layers, where each layer has the same update structure as the original algorithm but the parameters are now learned from data. This approach was later successfully extended to several iterative algorithms that solve problems like blind deblurring [2]}, non-negative matrix factorization [3]}, semantic image segmentation [4]}, clutter suppression [5]}, rain removal [6]} and source separation [7]}.
A standard practice in the above frameworks is to parameterize the function of interest using multi-layer perceptrons (MLPs) or convolutional neural networks (CNNs) [8]}.
However, MLPs and CNNs – which have proven to be tremendously effective in processing images, texts, and audio – are not quite suitable for problems in wireless communication.
In particular, the performance of these methods degrades dramatically when the network size becomes large since MLPs and CNNs fail to exploit the underlying topology of wireless networks.
This has led to several approaches that tried to adjust CNNs to the wireless setting [9]}, [10]}, [11]} capitalizing on, e.g., the spatial disposition of wireless networks [12]}.
We adopt an alternative direction [13]}, [14]}, [15]}, where graph neural networks (GNNs) [16]}, [17]}, [18]}, [19]}, [20]}, [21]}, [22]} are used to parameterize the power allocation function, thus leveraging the natural representation of wireless networks as graphs.
GNNs utilize the structural relationships between nodes to locally process instantaneous channel state information.
